Police have said for weeks their investigation will consider whether anyone should be charged with a crime.
A statement circulated to those involved said an "initial assessment" of seized material and witness statements had allowed police to reach the conclusion that each organisation may have committed the offence.
Yvette Williams, a coordinator at the Justice 4 Grenfell campaign group, said the move would help restore trust between the police and the community.
Both organisations will be questioned under the 2007 corporate manslaughter and corporate homicide act.
But he faced calls to resign as those in the room informed his panel that he was not representative of the Grenfell community.
'Gross negligence manslaughter carries a punishment of prison time, and I hope that the police and the CPS are considering charges of manslaughter caused by gross negligence'.
They added: "It's not a case of either one or the other for justice to be done and to be seen to be done we want both".More news: ICE arrests man in Forest
More news: Trump continues crusade against Sessions with a fresh line of attack
More news: Jerusalem crisis could have 'catastrophic costs — United Nations envoy
As the offence was not committed by an individual, no arrest would be made.
"People implement policy, people make decisions, people took particular actions and those people are responsible".
The leader of Wiltshire Council will be part of the taskforce undertaking the independent review of the Grenfell Tower fire disaster.
It will also support the council to significantly improve housing management, including by tackling problems in the tenant management organisation and making sure it develops a plan for the Grenfell Tower site - with correct leadership and governance arrangements in place to deliver the change.
Robert Back, chief executive of the management organisation, stepped down to "concentrate on assisting with the investigation and inquiry".
"Alongside the recovery operation in Grenfell Tower to find, recover and identify all those that died, we are conducting one of the largest criminal investigations outside of counter terrorism operations", Metropolitan Police said in the letter to residents.